To solve this problem, we need to find a common denominator for all the fractions. The least common denominator (LCD) for 2, 4, 8, 16, 3, and 64 is 64.

Now, let's convert each fraction to have a denominator of 64:

1/2 = 32/64
1/4 = 16/64
1/8 = 8/64
1/16 = 4/64
1/3 = 21/64
1/64 = 1/64

Now, we can add the fractions:

32/64 + 16/64 + 8/64 + 4/64 + 21/64 + 1/64

Adding the numerators together:

(32 + 16 + 8 + 4 + 21 + 1)/64

Simplifying the numerator:

(82)/64

Now, we can simplify the fraction:

82/64 = 41/32

Therefore, 1/2 + 1/4 + 1/8 + 1/16 + 1/3 + 1/64 = 41/32.